Migrate automation dialogs to dirty state provider and dialog behaviour

[timmo001]

Breaking change

Proposed change

Part of #52334

Screenshots

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New feature (thank you!)
• Breaking change (fix/feature causing existing functionality to break)
• Code quality improvements to existing code or addition of tests

Additional information

• This PR fixes or closes issue: fixes #
• This PR is related to issue or discussion: Update dialog / popover / sheet to follow new guideline #52334
• Link to documentation pull request:
• Link to developer documentation pull request:
• Link to backend pull request:

Checklist

• I understand the code I am submitting and can explain how it works.
• The code change is tested and works locally.
• There is no commented out code in this PR.
• I have followed the perfect PR recommendations
• Any generated code has been carefully reviewed for correctness and compliance with project standards.

If user exposed functionality or configuration variables are added/changed:

• Documentation added/updated for www.home-assistant.io

To help with the load of incoming pull requests:

• I have reviewed two other open pull requests in this repository.